The phenomenon of solitary wave was first observed by John Scott Russel [1]} almost two centuries ago, which is later used to characterize wave that does not disperse and retains its original identity as time evolves. Exact existence theory for solitary water waves, however, first appeared more than a century later in the work of Lavrentiev [2]}, Friedrichs-Hyers [3]}, and Ter-Krikorov [4]} for small-ampliltude irrotational waves. Construction for large-amplitude irrotational waves was achieved by Amick–Toland [5]}, [6]} and Benjemin–Bona–Bose [7]}.
